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The evolution of honeycomb

Honey-bees construct wax combs inside their nests. The combs are made of hexagonal prisms – cells – built back to back, and are used to store honey, nectar, and pollen, and to provide a nursery for bee larvae. The combs are natural engineering marvels, using the least possible amount of wax to provide the greatest amount of storage space, with the greatest possible structural stability. Darwin recognised that explaining the evolution of the honey-bee’s comb-building abilities was essential if his theory of natural selection was to be taken seriously, and in the 1850s he carried out his own experiments at his home at Down House in Kent, and wrote many letters on the subject.

For natural theologians, who looked on nature as showing the workings of providence, the bee cell was a favourite subject. The question of how little insects could solve correctly a design problem that challenged even expert human geometers, and implement it practically, pointed, they thought, to a governing intelligence. In Lord Brougham’s Dissertations on subjects connected with natural theology (1839), Brougham commented that bees acted with a discipline that in men could only be effected by a superintendent with a design. The bee chose the most advantageous shape for her cells, he wrote, ‘as indeed we might well suppose when we recollect who is her teacher’ (Brougham 1839, 1: 35, 77). William Kirby wrote of the bees as ‘those Heaven-instructed mathematicians, who before any geometer could calculate under what form a cell would occupy the least space without diminishing its capacity, and before any chemist existed to discover how wax might be elaborated from vegetable sweets, instructed by the Fountain of Wisdom, had built their hexagonal cells of that pure material, had closed them at the bottom with three rhomboidal pieces, and were enabled, without study, so to construct the opposite story of combs, that each of these rhomboids should form one of those of three opposed cells, thus giving strength to the structure, that in no other place, could have been given to it’ (Kirby 1852, 2: 246).

Darwin’s copy of Brougham’s Dissertations is heavily annotated. He recognised that the problem of the bee cell was important for his theory. On page 77, he scribbled, ‘very wonderful – it is as wonderful in the mind as certain adaptations in the body – the eye for instance, if my theory explains one it may explain other.’ Darwin, and others working on naturalistic explanations, needed to show how bee cells could arise from simple processes. The theory of evolution by natural selection was supposed to be a comprehensive theory of life on earth: if it could not explain bee cells, it was radically flawed. Darwin needed to show two things: first, how the bees’ abilities had evolved over time, and second, how the bees built their combs using only the instincts and intelligence they had evolved.

The first point was relatively straightforward. Brougham, rejecting the suggestion that hexagonal cells could have arisen from cylindrical cells, asserted that no bee in the world ever made cylindrical cells (Brougham 1839, 1: 32). However, Darwin knew that humble bees made roughly cylindrical or near spherical cells for holding honey and larvae, and was delighted to discover a Mexican bee, Melipona domestica, that made a rough comb of cylindrical or nearly spherical cells, with flat sides where cells happened to meet. Most naturalists accepted that circular structures were the easiest for animals to construct: for example, birds’ nests are usually circular. Darwin argued that if the Melipona put its cells together in a more regular fashion, it would probably develop a structure like that of the honey-bee (Origin, p. 226). Further, there were advantages to a more regular, hexagonal-celled, structure: it used less wax to store more honey. Thus, when under environmental pressure (cold winters, lack of food), bee colonies with the more efficient structure would be more likely to survive and prosper.

The second point, how bees actually built the comb, involved Darwin in a great deal of correspondence and experimentation. When he began working in earnest on the subject for a projected book on the species question, Darwin wrote to George Robert Waterhouse. Waterhouse had written the article on bees for the Penny Cyclopaedia in 1835. He suggested that bees acted according to two antagonistic principles: one causing them to deposit and excavate the wax, the other limiting the degree of excavation. In his view, bees set out to make circular cells, which became hexagonal due to their working under the constraints of the two antagonistic principles and the proximity of other cells. Darwin’s letter has not been found, but from Waterhouse’s reply, it is clear that Darwin was asking for examples of honey-bees making cylindrical structures, either free-standing or at the edges of combs where the cells were not subject to the space constraints of other cells. (Letter from G. R. Waterhouse, 14 April 1857.)

In a later letter Waterhouse gave a detailed account of his observations of a leaf-cutter bee making a circular structure out of clay. After giving the matter due consideration he had realised that the repetitive motions of the bee, which he had at first thought ‘stupid’, were in fact guaranteed to produce a regular circular structure. ‘By keeping the body fixed in one position for some time & by working in all directions as far as she could reach, in her excavating, she would necessarily form a cavity in segments of circles and of definite size— —the diameter being determined by her power of reaching.’ (Letter from G. R. Waterhouse, 10 February 1858.)

By now not only Waterhouse but William Bernhard Tegetmeier (who had helped Darwin with his work on pigeons) and other members of the Entomological Society of London were exercising their minds on the problem. In his next letter, Waterhouse described wasps’ nests exhibited at a meeting of the society. It had been objected to his theory of cell-building that wasps also built combs of hexagonal cells, even though to begin with only one wasp (the queen) worked on the comb. Waterhouse responded that the wasp working alone always worked on several cells at once, and so was subjected to the same formal constraints as a group of bees working together. (Letter from G. R. Waterhouse, 13 February 1858.)

In April 1858, Darwin went to London to meet William Hallowes Miller, a crystallographer, to discuss the geometry of bee cells. Miller had developed a system of crystallography that was ‘far more simple, symmetrical, and adapted to mathematical calculations than any which had yet been devised’ (ODNB). Possibly Darwin consulted Miller simply on geometry, but his choice of expert suggests an interest in how a complex pattern may arise from natural forces. Darwin made notes for their discussion in a memorandum to W. H. Miller, [15 April 1858], summarising his position as follows:

Bees can make apparently true cylinders & spheres. (2) They never begin one cell at time always several (3) they can judge distance to certain extent, & (4) those that make their spheres or cylinders so that if completed, would intersect make an intermediate flat wall. Then assume perfect judge of distance, I thought that all angles might follow, for I cd see they would in hexagonal prism.–— My notion modification of Waterhouses. Ld. Brougham sneers at it.

Meanwhile, Waterhouse was still exercising his mind on the subjects of wasp’s nests. He sent another long letter to Darwin on the subject, this time arguing that where the sides of wasp cells that were not bounded by other cells were straight, this was because of the cues taken by the wasps from the other straight sides that were bounded by other cells (letter from G. R. Waterhouse, 17 April 1858).

Waterhouse also told Darwin of a meeting at the Entomological Society of London on 5 April. Since the notes he promised to send Darwin have not been found, the account given in the Proceedings of the Entomological Society of London n.s. 5: 17–18 is reproduced here:

Some discussion having arisen relating to the construction of the cells of the hive bee, Mr. Waterhouse stated that he was of opinion that the hexagonal form of cell was accidental, so far as the constructors of the cell were concerned; and having been called upon to explain his views, he proceeded, in the first place, to call attention to the fact that if a number of cylinders of equal size were packed close together, side by side, each cylinder would be surrounded by six others; that, assuming the cylindrical form (or at least a form of cell approaching more or less to the cylindrical, and having a circular section) was the type form of isolated cells constructed by different kinds of bees, and that, in the case of the hive bee, a number of insects worked together, first depositing a small portion of wax, then excavating a small circular cavity in the same, for the commencement of a cell; this then being followed by the deposition of more wax and the excavation of more cavities, and these being placed close to the first; then neither of the cells could be constructed of their natural diameter, provided the first cavity formed had not attained the full diameter of the complete cell. The diameters of the cells would intersect each other; but if partitions be left between them, the cell must be six-sided, if the cells remain equal in size. In order to make the idea more clear, he . . . would assume for a moment that it were a law that a number of equal-sized circles, being packed closely together, side by side, and that each circle was then surrounded by seven others; he believed that the cell of the hive bee would, in that case, have been seven-sided. Such were the views entertained many years back by Mr. W., and published by him in the ‘Penny Cyclopaedia;’ and having subsequently had his attention particularly directed to the subject, whilst examining the nests of a vast number of Hymenopterous insects, he still believes those views to be essentially correct. He now, however, has reason to believe that it is not absolutely necessary for the supposed natural diameters of the cells to intersect before an angular-formed cell would be produced. The instinct which leads an insect to excavate, in order to form a cell, may lead it to excavate beyond what would be necessary to form a sufficiently large cell, in the case of an insect, which, under ordinary circumstances, burrows until it comes in contact with an adjoining cell. Contact with other cells was the essential condition which influenced the angular form of any particular cell. . . . Mr. Waterhouse said he had possessed a very small nest of a hornet which consisted of three cells only; it was built in a small cavity adjoining a large nest, and where there was not room for more than three cells; they were circular externally and angular internally,–—that is to say, each cell had two straight sides where it came in contact with two other cells, and was rounded elsewhere. Mr. Tegetmeier remarked that he possessed a small piece of honey-comb which presented the same peculiarities.

Darwin quickly arranged to look at Tegetmeier’s piece of honeycomb (letter to W. B. Tegetmeier, [21 April 1858]); however, it had been mislaid. Nevertheless, Darwin asked Tegetmeier to keep an eye out for the first beginnings of the comb (letter to W. B. Tegetmeier, 9 May [1858]). He suspected that the first cells, built without the constraints of neighbouring cells, would not be hexagonal.

At this time Darwin was much exercised by the work of François Huber. In his copy of Huber 1814, 2: 143, he scribbled a note: ‘If the sides of separate cell one are angular before other cells formed fatal to my theory.’ He wrote to his son William, ‘I am come to heavy grief about my Bees-cells & my only hope is that Huber has not correctly described their manner of building’ (letter to W. E. Darwin, [26 May 1858].) To Tegetmeier, he explained in more detail:

Huber says that first, a very thin & very low little ridge is made; & then on one face the base of a single cell is hollowed out, & on the opposite face, the bases of two cells. He states that first the outlines of these 3 primordial cells are arched, (section [DIAGRAM OF CURVED ARCH] ) & then made angular ( [DIAGRAM OF POINTED ARCH] ). Now what I what I want so much to see is this rudiment of the comb in this state. I believe when the arched bases of the cells are made angular, the bases of other adjoining cells have just been commenced. The hexagonal tube or prism has not been at this period hardly been begun; & all must be very minute. (See the letter)

Darwin was probably particularly concerned about the pentagonal cell wall that is constructed out of the original curved arch, since Huber’s diagrams show this transition clearly. Darwin thought that the arch was not made angular until the hexagonal cells of the second row had been begun by the bees making further hemispherical scrapes. However, he may also have been concerned about the angular bottoms of the cells that were excavated out of the original hemispherical scrapes. The bottom of a hexagonal cell is a pyramidal structure that fits neatly against the bottoms of three cells on the other side of the wall. Darwin thought that this angular structure too was only formed as a result of the presence of other cells.

Challenging Huber was a serious business; he had laid the scientific foundations of the study of the honey-bee, despite being blind from the age of 15. His work was carried on with the help of his wife and manservant, and depended on minute, repeated observations. He too was sceptical about the view of the bee as master geometrician; explaining how the necessary angles might arise from the initial circular workings of the bee, he asked, ‘May we not deduce from the preceding facts, that the geometry, which apparently embellishes the productions of these insects, is rather the necessary result than the principle of their proceedings?’ (Huber 1841, p. 269.)

Darwin asked Tegetmeier to observe the beginning of the comb and, having been lent a glass hive by a friend, did the same himself; he also asked Tegetmeier to look out for isolated cylindrical cells (letter to W. B. Tegetmeier, 5 June [1858]). Tegetmeier suggested putting a piece of wax in the hive for the bees to work on. Using this method, Darwin ‘got some excavated hemispherical bases in artificial wax—hurrah!’ and was thinking of ordering another hive from Tegetmeier, and buying a swarm (letter to W. B. Tegetmeier, 8 [June 1858]). (Articial wax is probably beeswax, but a block of wax added to the hive rather than wax that the bees in hive were producing and working themselves.)

Darwin tried three different experiments with bees’ cells at Down that he reported in Origin. In one, he put a thick block of wax into the hive. ‘The bees instantly began to excavate minute circular pits in it: and as they deepened these little pits, they made them wider and wider until they were converted into shallow basins, appearing to the eye perfectly true or parts of a sphere, and of about the diameter of a cell. It was most interesting to me to observe that wherever several bees had begun to excavate these basins near together, they had begun their work at such a distance from each other, that by the time the basins had acquired the above stated width (i.e. about the width of an ordinary cell), and were in depth about one sixth of the diameter of the sphere of which they formed a part, the rims of the basins intersected or broke into each other. As soon as this occurred, the bees ceased to excavate, and began to build up flat walls of wax on the lines of intersection between the basins, so that each hexagonal prism was built upon the festooned edge of a smooth basin, instead of on the straight edges of a three-sided pyramid as in the case of ordinary cells.’ (Origin, p. 223.) The cells were built up in a hexagonal shape when their bases intersected with those of other cells; but the pyramidal bases were apparently not built, since there was no pressure to accomodate cells on the other side of the wax, which was a thick block.

These experiments were repeated in 2009 by John Williams, a master beekeeper who maintains an observation hive at Down House during the summer. In these photographs, it is possible to see how the bees tended to clump their cells and build them up into hexagons; but the circular foundations of seven adjacent unfinished cells are also visible in the second photograph next to the left-hand clump of cells.

Secondly, Darwin put a thin piece of vermilion wax in the hive, a ‘narrow, knife-edged ridge’.

The bees instantly began on both sides to excavate little basins near to each other . . . ; but the ridge of wax was so thin, that the bottoms of the basins, if they had been excavated to the same depth as in the former experiments, would have broken into each other from the opposite sides. The bees, however, did not suffer this to happen, and they stopped their excavations in due time; so that the basins, as soon as they had been a little deepened, came to have flat bottoms; and these flat bottoms, formed by thin little plates of the vermilion wax having been left ungnawed, were situated, as far as the eye could judge, exactly along the planes of imaginary intersection between the basins on the opposite sides of the ridge of wax. In parts, only little bits, in other parts, large portions of a rhombic plate had been left between the opposed basins, but the work, for the unnatural state of things, had not been neatly performed. (Origin, pp. 229–30.)

In other words, by starting their excavations in the correct places, the bees produced an approximation to the pyramidal bottoms of cells simply by ceasing to excavate when they were about to break through into another cell.

In his third experiment, Darwin covered edges of the walls of a hexagonal cell, or the extreme margin of a growing comb – the place in which the cells are furthest from hexagonal – with a thin layer of vermilion wax.

‘I invariably found that the colour was most delicately diffused by the bees . . . by atoms of the coloured wax having been taken from the spot on which it had been placed, and worked into the growing edges of cells all around’ (Origin, p. 232).

The bees were continually rebuilding unsatisfactory cells as the comb grew outwards.

The experiments with vermilion wax have also been repeated by John Williams. A ‘knife-edge’ ridge of wax is sometimes applied to the top bar of a hive to encourage the bees to build in the right place, and it is likely that the ‘knife-edged ridge’ used by Darwin was a similar arrangement. The results of this experiment show something that Darwin does not mention, but that beekeepers would no doubt take for granted: the bees add their own wax to the vermilion wax as they work to extend it. The vermilion (as Darwin found in his third experiment) becomes thoroughly mixed with uncoloured beeswax over most of the resulting comb. This is now an on-going experiment and can be seen in the observation hive at Down House during the summer. The result is shown in the photograph below.

In August 1858, Waterhouse’s remarks at the 5 April meeting of the Entomological Society (see extended quotation, above) were reprinted in theZoologist. He no doubt began to regret the wording of his suggestion that hexagonal cells were a necessary consequence of packing cylinders in a small space, as some readers may have understood him to mean that the hexagons were formed as a result of lateral pressure on the comb, a theory that had been current and that had been dismissed by Lord Brougham. At a meeting of the Entomological Society on 7 July 1858 (Proceedings of the Entomological Society of London n.s. 5 (1858–61): 34–5), the issue was discussed. John Edward Gray, the president, using vermicelli as an analogy, supported the idea that compressed cylinders became hexagonal prisms, and added, with characteristic acerbity, that he ‘considered the attempt made by Natural Theologians to prove that the formation of an hexagonal rather than a cylindrical cell indicated the possession of a greater degree of Divine wisdom bestowed on the insect, was the greatest piece of humbug they had ever brought forward.’Frederick Smith however had apparently made paper cylinders and failed to compress them into hexagons. Waterhouse reviewed the latest controversies in his letter to Darwin of 2 August 1858. The notion that the theory of hexagonal bee cells being formed from cylinders depended on actual physical compression was to dog responses to Darwin’s own theory as well.

Also in August Darwin received a hive from Jamaica, and observed that the cells were larger than those made by European bees. He at once sent for specimens of the actual bees, probably curious to see whether the size of the cell was proportionate to the size of the bee. This would suggest that the famous regularity of bee cell sizes might have a simple explanation. (Letter to Richard Hill, 8 August [1859].) Much later, Jeffries Wyman wrote to Darwin from Cambridge, Massachusetts, that he found that bee cells were not as regular as some had supposed them to be; their measurements varied, the pyramidal bases of the cells sometimes had four, not three rhombs, and the transition from worker to drone cells (these are different sizes) was carried out in different ways (letter from Jeffries Wyman, 11 January 1866).

Concurrently with his work on cell formation, Darwin was thinking about why the hexagonal structure was advantageous to bees. It was already well known that the hexagonal cells stored the greatest possible amount of honey and pollen with the least possible expenditure of wax, but in September 1858 Tegetmeier was able to give Darwin figures for just how costly wax production was to bees. He calculated that 15lb of sugar was consumed in the secretion of 1lb of wax. Tegetmeier also confirmed Darwin’s conclusions about the building of cells. (Letter to W. B. Tegetmeier, 8 September [1858].)

In Origin, in November 1859, Darwin published a theory of cell-building that differed from both Huber’s and Waterhouse’s. Huber had believed that although the bees began by making curved arches in the wax partly following the outline of the first hemispherical depressions that they dug into the wall of wax, these were swiftly converted into angular (pentagonal) structures and followed in the second row by hexagonal structures. Waterhouse believed that the bee built the cells up in circles, and that when the circle of one bee threatened to break into the circle of another, they both stopped excavating at the nearest point and switched their attention to excavating the wax where there was no imminent danger of breaking through, thus making hexagons. Darwin, however, had observed that the bees began by making hemispherical scrapes in the wax, and that where the scrapes intersected, they built or excavated straight walls, thus building up hexagonal prisms. Cells at the edge of the comb tended to have roughly curved walls until further cells were built and they were transformed into more regular hexagons.

Thus, in Origin, Darwin explained the development of the honey-bee’s cell-building instinct from simpler forms (the less organised, round cells of other insects), and explained their method of building based on the repetition of simple actions and feedback from simple sensations, rather than on the application of geometry. His observations, and those of Tegetmeier and others, had proved that bees did not build angular structures except at the intersections between cells; that they continually rebuilt the roughly finished cells at the margins of the comb into more regular structures as the comb grew outwards; that there were measurable advantages to the regular structures of the honey-bee over the more haphazard structures of other bees in times of scarcity; and that the unfailing regularity and precision of the bee cell was, when precise measurement was bought to bear, a myth.

In 1865, Darwin received a letter from Edward Cresy (letter from Edward Cresy, 10 September 1865), in which Cresy sent as an illustration of Darwin’s bee-cell theory a description of a plum pie, the crust of which came out of the oven ‘completely mapped out with hexagonal articulations’. ‘By guesswork each plumb should have punched just a swelling & then a round hole for itself like a round shot through a plank but I suppose the strain came to equally on all part of the crust so the spherical plumbs laid the foundation, without any instinctive knowledge of a series of regular hexagonal combs’, Cresy concluded: the plums didn’t need to know how to do it any more than the bees did.